Question

Chu, Singfat (1996, Diamond ring pricing using linear regression, Journal of Statistical Education 4(3)) studied prices of diamond rings changing with the weights of their diamond stones. Only 20K ladies' rings, each mounted with a single diamond stone, were considered in the study. 20K rings are made with gold of 20 carat purity (Pure gold is rated as 24K). There were 48 such rings of varying designs. The weights of the diamond stones ranged from 0.12 to 0.35 carat (a one carat diamond stone weighs 0.2 gram) and were priced between $223 and $1086.

Carat: 0.17, 0.16, 0.17, 0.18, 0.25, 0.16, 0.15, 0.19, 0.21, 0.15, 0.18, 0.28, 0.16, 0.20, 0.23, 0.29, 0.12, 0.26, 0.25, 0.27, 0.18, 0.16, 0.17, 0.16, 0.17, 0.18, 0.17, 0.18, 0.17, 0.15, 0.17, 0.32, 0.32, 0.15, 0.16, 0.16, 0.23, 0.23, 0.17, 0.33, 0.25, 0.35, 0.18, 0.25, 0.25, 0.15, 0.26, 0.15

Price: 355, 328, 350, 325, 642, 342, 322, 485, 483, 323, 462, 823, 336, 498, 595, 860, 223, 663, 750, 720, 468, 345, 352, 332, 353, 438, 318, 419, 346, 315, 350, 918, 919, 298, 339, 338, 595, 553, 345, 945, 655, 1086, 443, 678, 675, 287, 693, 316

Some summary statistics of the data are given as follows.

	Mean	Standard Deviation	Correlation Coefficient (r)
Carat	0.2042	0.0568	0.9891
Price	500.0833	213.6428

Q1. What are the explanatory and response variables in this study?

Q2. Calculate the coefficient of determination or r 2 and write a sentence to interpret the value of r 2 in the context of this application.

Q3. Find the least-square regression equation relating the response variable to the explanatory variable using their means, standard deviations, and correlation coefficient. Show details

Q4. ) Write a sentence to interpret the slope of the regression equation in Q3 in the context of this study.

Q5. According to the regression equation in Q3, what is the average price for a 20K ladies' ring of 0.30 carat?

Answer 1